Who qualifies the adequate quality of evidence and on which bases?
Ideally, people with relevant expertise. In the real world, it's often people without. The bases depend on the nature of the evidence, e.g. ranging from remote hearsay to the results of well designed & controlled experiment. For the former, priors alone will determine the assessment; for the latter, examination of the hypothesis, design, methodology, data analysis and conclusions will complement the priors.
You can start with "Dark Matter", for example, or any other distant theorized entities or properties derived from scientific necessity for something to be there to hold explanations together.
Dark Matter isn't an explanation, it's a label for unexplained observations under investigation ('Dark' because it doesn't radiate, 'Matter' because it behaves like a distribution of mass). In what sense do you think it's supernatural? It isn't something to hold explanations together, it's observation that needs explanation.
Sure, but by such means of demarcation you are disqualifying things that we've never experienced and can't will not experience directly.
I'm not disqualifying anything - that can only be done by explicit falsification; there's a difference between assessing a low probability and disqualification. In the case of claims of the miraculous, paranormal, or supernatural, there are often mundane explanations with a high prior probability. They may appear to devalue or disqualify the claim, but they are explanations of it; conversely, the descriptive labels 'miraculous', 'paranormal', or 'supernatural' explicitly deny explanation.
Strings like strings in string theory would have to be discarded outright by means of your logic..
Not at all. String Theory is an extended model or framework based on the mathematics of our most successful physical model - as such it's priors are impeccable.
Typically, in philosophy of science, the elegance of explanations trumps the evidence.
I don't agree; for example, Feynman and Gell-Mann both said that theoretical elegance is an important consideration, and should be taken into account, but Feynman famously said, "
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
By calling it "collective subjective" you are not really getting rid of the problem, you merely distribute it among larger population.
Who called it "collective subjective" other than you?